Geometry and measures worksheet — GCSE Foundation

1.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

2.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

3.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

4.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

5.Write down the exact value of tan 0°.

6.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

7.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

8.Write down the name given to a triangle whose three sides are all the same length.

9.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

10.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

11.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?

12.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

13.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.

14.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

15.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.